The occurrence of large amplitude roll motions of modern ships represents a considerable threat to goods and life in today's navigation. Especially indirect excitation mechanisms in head or following seas lead to large roll responses. The irregularity of ocean waves gives rise to sudden and unpredictable growth of the roll amplitude. This phenomenon is illustrated by the investigation of an indirectly excited nonlinear oscillator describing the ship roll motion. We further discuss possible models for wave excitation processes and highlight future tasks for scientific computing in the field of probabilistic ship dynamics.